# Brownian Dynamics at Boundaries and Interfaces

## In Physics, Chemistry, and Biology

Part of the Applied Mathematical Sciences book series (AMS, volume 186)

Part of the Applied Mathematical Sciences book series (AMS, volume 186)

Brownian dynamics serve as mathematical models for the diffusive motion of microscopic particles of various shapes in gaseous, liquid, or solid environments. The renewed interest in Brownian dynamics is due primarily to their key role in molecular and cellular biophysics: diffusion of ions and molecules is the driver of all life. Brownian dynamics simulations are the numerical realizations of stochastic differential equations that model the functions of biological micro devices such as protein ionic channels of biological membranes, cardiac myocytes, neuronal synapses, and many more. Stochastic differential equations are ubiquitous models in computational physics, chemistry, biophysics, computer science, communications theory, mathematical finance theory, and many other disciplines. Brownian dynamics simulations of the random motion of particles, be it molecules or stock prices, give rise to mathematical problems that neither the kinetic theory of Maxwell and Boltzmann, nor Einstein’s and Langevin’s theories of Brownian motion could predict.

This book takes the readers on a journey that starts with the rigorous definition of mathematical Brownian motion, and ends with the explicit solution of a series of complex problems that have immediate applications. It is aimed at applied mathematicians, physicists, theoretical chemists, and physiologists who are interested in modeling, analysis, and simulation of micro devices of microbiology. The book contains exercises and worked out examples throughout.

Application to channel simulation Brownian dynamics simulation at boundaries Stochastic model of a non-Arrhenius reaction The Langevin equation Trajectories, fluxes, and boundary concentrations

- DOI https://doi.org/10.1007/978-1-4614-7687-0
- Copyright Information Author 2013
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-1-4614-7686-3
- Online ISBN 978-1-4614-7687-0
- Series Print ISSN 0066-5452
- Series Online ISSN 2196-968X
- About this book